“Elimelech.” The name means, “My God is King.” Elimelech is the only person in the Bible with that name. It is worth noting that the name is also found in the El-Amarna letters, and in a pagan context can mean “El is Milku” but that is highly unlikely in Bethlehem.
“Naomi.” “Naomi” means “pleasant” or “my pleasure.” The names of the two sons are more difficult to determine.
“Mahlon and Chilion.” The meanings of the names Mahlon and Chilion are difficult to determine with certainty. However, it is likely that Mahlon is from malah, “to be sick, to be weak,” and Chilion is from kalah, “to come to an end” thus “to be frail.” It is possible that those were the names actually given to the children when they were named because they were weak and frail. Children were not named at birth. Male children were usually named when they were circumcised at 8 days old. It is also possible that these “names” were given to them due to their characteristics as they grew up, in a sense like nicknames based on character and behavior. It is common that names in the Bible tell us about the character or circumstances of the person and was not the person’s given name. For example, “Job” basically means “attacked one,” and would not have been his given name but a name he was called after his horrible ordeal in losing his children, wealth, and health. In any case, the names point to the circumstances of the boys and so it was no surprise to the Hebrew reader that they died when very young.
“Ephrathites of Bethlehem Judah.” That both Elimelech and Naomi were “Ephrathites” means they were locals. They were born and raised in the Bethlehem area. “Ephrath” (or Ephrathah, Micah 5:2) means “fruitful,” but exactly what it refers to is debated. It could be another name for Bethlehem (and was likely used that way), or the area around Bethlehem, or a small village very close to Bethlehem, or perhaps the name of a clan that lived in Bethlehem or the general area. Ephrath was often identified with Bethlehem (Gen. 35:19; Ruth 4:11; Micah 5:2). We see from the Book of Ruth that although Naomi was an Ephrathite, she lived in Bethlehem.